handa (nh5757) – HW01 – meth – (55830)
1
This
printout
should
have
6
questions.
Multiplechoice questions may continue on
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before answering.
001
10.0points
Below is the graph of a function
f
.
2
4
6

2

4

6
2
4
6
8

2

4
Use the graph to determine
lim
x
→ 
5
f
(
x
).
1.
lim
x
→ 
5
f
(
x
) = 6
2.
lim
x
→ 
5
f
(
x
) = 9
3.
lim
x
→ 
5
f
(
x
) = 3
correct
4.
lim
x
→ 
5
f
(
x
) does not exist
5.
lim
x
→ 
5
f
(
x
) = 4
Explanation:
From the graph it is clear the
f
has both
a left hand limit and a right hand limit at
x
=

5; in addition, these limits coincide.
Thus
lim
x
→ 
5
f
(
x
) = 3
.
002
10.0points
When
f
is the function defined by
f
(
x
) =
braceleftbigg
5
x

1
, x <
1 ,
4
x

1
, x
≥
1
,
determine if
lim
x
→
1

f
(
x
)
exists, and if it does, find its value.
1.
limit = 5
2.
limit = 3
3.
limit = 4
correct
4.
limit does not exist
5.
limit = 2
6.
limit = 6
Explanation:
The left hand limit
lim
x
→
1

f
(
x
)
depends only on the values of
f
for
x >
2.
Thus
lim
x
→
1

f
(
x
) =
lim
x
→
1

5
x

1
.
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 Spring '10
 Gualdini
 Limit, lim, Limit of a function

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